Showing papers on "ω-automaton published in 1989"

On the limit sets of cellular automata

Abstract: The limit sets of cellular automata, defined by Wolfram, play an important role in applications of cellular automata to complex systems. A number of results on limit sets are proved, considering both finite and infinite configurations of cellular automata. The main concern of this paper is with testing membership and (essential) emptiness of limit sets for linear and two-dimensional cellular automata.

On Ω-automata and temporal logic

Abstract: We study here the use of different representation for infinitary regular languages in extended temporal logic. We focus on three different kinds of acceptance conditions for finite automata on infinite words, due to Buchi, Streett, and Emerson and Lei (EL), and we study their computational properties. Our finding is that Buchi, Streett, and EL automata span a spectrum of succinctness. EL automata are exponentially more succinct than Buchi automata, and complementation of EL automata is doubly exponential. Streett automata are of intermediate complexity. While translating from Streett automata to Buchi automata involves an exponential blow-up, so does the translation from EL automata to Streett automata. Furthermore, even though Streett automata are exponentially more succinct than Buchi automata, complementation of Streett automata is only exponential. As a result, we show that the decision problem for ETLEL, where temporal connectives are represented by EL automata, is EXPSPACE-complete, and the decision problem for ETLS, where temporal connectives are represented by Streett automata, is PSPACE-complete.

Theory of Finite Automata With an Introduction to Formal Languages

Abstract: When there are many people who don't need to expect something more than the benefits to take, we will suggest you to have willing to reach all benefits. Be sure and surely do to take this theory of finite automata with an introduction to formal languages that gives the best reasons to read. When you really need to get the reason why, this theory of finite automata with an introduction to formal languages book will probably make you feel curious.

Order of the transition versus space dimension in a family of cellular automata.

Abstract: A mean-field theory of (probabilistic) cellular automata is developed and used to select a typical local rule whose mean-field analysis predicts first-order phase transitions. The corresponding automaton is then studied numerically on regular lattices for space dimensions d between 1 and 4. At odds with usual beliefs on two-state automata with one absorbing phase, first-order transitions are indeed exhibited as soon as dg1, with closer quantitative agreement with mean-field predictions for high space dimensions. For d=1, the transition is continuous, but with critical exponents different from those of directed percolation.

Finite Automata, Their Algebras and Grammars: Towards a Theory of Formal Expressions

Abstract: 1 Concepts and Notations in Discrete Mathematics.- 2 The Structure Theory of Transition Algebras.- 3 The Structure and Behavior of Finite Automata.- 4 Transition Systems and Regular Events.- 5 Regular Canonical Systems.- 6 General Algebras: How They Function as Tree Acceptors and Push-down Automata.- 7 General Alphabets: The Theory of Push-down Automata and Context-free Languages.- Conclusion.- List of Symbols.- References.

On simultaneously determinizing and complementing omega -automata

Abstract: The authors give a construction to determine and complement simultaneously a Buchi automaton in infinite strings, with an exponential blowup in states and a linear blowup in the number of pairs. An exponential lower bound is already known. The previous best construction was double exponential. The present result permits exponentially improved essentially optimal decision procedures for various modal logics of programs. It also gives exponentially improved conversions between various kinds of omega automata. >

Automata Theory for Database Theoreticans.

Abstract: Abstract I describe several applications of automata theory to the analysis of Datalog programs, ranging from the easy to the difficult, in the hope of convincing the reader that automata theory provides a powerful set of abstractions and tools to database theoreticians.

The equivalence and learning of probabilistic automata

Abstract: It is proved that the equivalence problem for probabilistic automata is solvable in time O((n/sub 1/+n/sub 2/)/sup 4/), where n/sub 1/ and n/sub 2/ are numbers of states of two given probabilistic automata. This result improves the best previous upper bound of coNP. The algorithm has some interesting applications, for example, to the covering and equivalence problems for uninitiated probabilistic automata, the equivalence and containment problems for unambiguous nondeterministic finite automata, and the path-equivalence problem for nondeterministic finite automata. Using the same technique, a polynomial-time algorithm for learning probabilistic automata is developed. The learning protocol is learning by means of queries. >

The bit full-decomposition of sequential machines

Abstract: Control units and serial processing units of today's information processing systems must realize complex processes, which are usually described in the form of a sequential machine or a number of cooperating sequential machines. Large machines are difficult to: design, optimize, implement and verify. Therefore, there is a real need for CAD tools, which could decompose a complex sequential machine into a number of smaller and less complicated partial machines. For many years, the decomposition of only the internal states of sequential machines has been studied. However, this sort of decomposition is not a sUfficient solution. The complexity of a circuit implementing a sequential machine is a function not only of machine's internal states but as well of inputs and outputs. Furthermore, the possibility to implement a machine with today's array logic building blocks depends not only on the number of internal states but as well on inputs and outputs. So, there is a real need for decompositions upon the states, inputs and outputs of a sequential machine, i.e. for fulldecompositions. During the full-decomposition process, the input and/or state and/or output symbols (values) can be decomposed or the input and/or state and/or output bits. So, it is possible to perform the symbol fulldecomposition or the bit full-decomposition. This report provides the classification of full-decompositions and describes briefly the theoretical foundations of bit fulldecomposition. Comparing to the symbol full-decomposition,the bit fulldecomposition has the following advantage: input and output decoders are reduced to an appropriate distribution of the primary input and output bits between the partial machines. In the report, definitions of a bit partition and bit partition pairs are introduced and their usefulness to bit full-decompositions is shown. It is proved, that the bit full-decomposition can be treated as a special case of the symbol full-decomposition; therefore, no new decomposition theory is needed for this case, but the symbol fulldecomposition theory together with the theorems introduced here constitute the theory of bit full-decomposition. Finally, a comparison is made between the symbol and the bit fulldecompositions and some practical conclusions and remarks are presented. In the appendix, an example is provided that illustrates the possibility and the practical usefulness of bit full-decomposition. Based on the developed theory, the CAD algorithms calculating different bit full-decompositions have been developed and implemented. Those algorithms and the practical results are presented and estimated in the separate paper [5]. Index Terms Automata theory, decomposition, logic design, sequential machines. Acknowledgements The author is indebted to Prof. ir. A. Heetman and Prof. ir. M. P.J. Stevens for making it possible to perform this work, to Dr. P.R. Attwood for making corrections to the English text and to mr. C. van de Watering for typing the text.

The Synchronization of Nonuniform Networks of Finite Automata (Extended Abstract)

Abstract: The generalized firing squad synchronization problem (GFSSP) is the well-known firing squad synchronization problem extended to arbitrarily connected networks of finite automata. When the transmission delays associated with the links of a network are allowed to be arbitrary nonnegative integers, the problem is called GFSSP-NUD (GFSSP with nonuniform delays). A solution of GFSSP-NUD is given for the first time. The solution is independent of the structure of the network and the actual delays of the links. The firing time of the solution is bounded by O( Delta /sup 3/+ tau /sub max/), where tau /sub max/ is the maximum transmission delay of any single link and Delta is the maximum transmission delay between the general and any other node of a given network. Extensions of GFSSP and GFSSP-NUD to networks with more than one general are presented.<>

Epsilon-optimal discretized pursuit learning automata

Abstract: The authors consider the problem of a stochastic learning automaton interacting with an unknown random environment. The fundamental problem is that of learning, through interaction, the best action (that is, the action which is rewarded optimally) allowed by the environment. By using running estimates of reward probabilities to learn the optimal action, an extremely efficient pursuit algorithm was obtained by M.A.L. Thathachar et al. (1986, 1989) which is presently among the fastest-growing algorithms known. In the present work, the authors investigate the improvements gained by rendering the pursuit algorithm discrete. This is done by restricting the probability of selecting an action to a finite and, hence, discrete subset of

The power of two-way deterministic checking stack automata

Abstract: It is well known that nondeterministic two-way checking stack automata recognize NSPACE( n ). We show that deterministic two-way checking stack automata have the same power as deterministic two-way two-head finite automata. The easy proof is based on the closure under inverse deterministic two-way GSM mappings of the deterministic two-way two-head finite automaton languages.

Three-dimensional cellular automata and VLSI applications

Abstract: Finite, three-dimensional (3-D), N*(N*N) cellular automata with null boundary conditions are presented and discussed. It is shown that, depending on their local rule and the dimension N, these cellular automata exhibit group or semigroup algebraic structures similar to those in the one and two-dimensional (2-D) cases. The algebraic properties of these 3-D cellular automata are exploited in the implementation of integer modulo arithmetic units. Lower bounds on area A, time T, energy AT and AT/sup 2/ complexity metrics of 3-D cellular automata-based modulo arithmetic units are also presented. >

An upper bound on the order of locally testable deterministic finite automata

Abstract: A locally testable language is a language with the property that for some nonnegative integer k, called the order of locality, whether or not a word w is in the language depends on (1) the prefix and suffix of w of length k, and (2) the set of intermediate substrings of w of length k + 1, without regard to the order in which these substrings occur. The local testability problem is, given a deterministic finite automaton, to decide whether it accepts a locally testable language or not. Recently, we introduced the first polynomial time algorithm for the local testability problem based on a simple characterization of locally testable deterministic automata. This paper investigates the upper bound on the order of locally testable automata. It shows that the order of a locally testable deterministic automaton is at most n4 + 1, where n is the number of states of the automaton.

Linear Numeration Systems, Theta-Developments and Finite Automata

Abstract: In numeration systems defined by a linear recurrence relation, as well as in the set of developments of numbers in a non integer basis ϑ, we define the notion of normal representation of a number. We show that, taking for ϑ the greatest root of the characteristic polynomial of the linear recurrence, and under certain conditions of confluence, the normal representation can be obtained from any representation by a finite automaton which is the composition of two sequential transducers derived from the linear recurrence. The addition of two numbers can be performed by a left sequential transducer.

Automata on infinite objects and their applications to logic and programming

Abstract: We introduce various types of ω-automata, top-down automata and bottom-up automata on infinite trees. We study the power of determinstic and nondeterministic tree automata and prove that deterministic and non-deterministic bottom-up tree automata accept the same infinite tree sets. We establish a relationship between tree automata, Logic programs, recursive program schemes, and the monadic second-order theory of the tree. We prove that the equivalence of two rational logic programs is decidable.

On the Finite Degree of Ambiguity of Finite Tree Automata

Abstract: The degree of ambiguity of a finite tree automaton A, da(A), is the maximal number of different accepting computations of A for any possible input tree. We show: it can be decided in polynomial time whether or not da(A) 1 having a finite degree of ambiguity: for every input tree t there is a input tree t1 of depth less than 22n·n! having the same number of accepting computations; the degree of ambiguity of A is bounded by 222·log(L+1)·n.

Proof of a conjecture of R. Kannan

Abstract: R. Kannan conjectured that every non-deterministic two-way finite automaton can be positionally simulated by a deterministic two-way finite automaton. The conjecture is proved here by reduction to a similar problem about finite semigroups. The method and the result are then generalized to alternating two-way finite automata.

The Equivalence and Learning of Probabilistic Automata (Extended Abstract)

Abstract: We prove that the equivalence problem for probabilistic automata is solvable in time O((n1 + n2)4) , where RI and n2 are numbers of states of two given probabilistic automata. This result improves over the best previous upper-bound of coNP. This algorithm has some interesting applications to, for example, the covering and equivalence problems for uninitiated probabilistic automata, the equivalence and containment problems for unambiguous nondeterministic finite automata and the path equivalence problem for nondeterministic finite automata. Using the same technique, we present a polynomial-time algorithm for learning probabilistic automata. Our learning protocol is learning via queries.

The object-oriented paradigm and automata theory

Abstract: The concepts in the object-oriented paradigm are examined using automata theory. A dynamic model is proposed which serves as a frame within which these concepts are explored. Central to the model is the class automaton which represents the object-oriented class.